Publications

We present a comprehensive study of enantioselective orientation of chiral molecules excited by a pair of delayed cross-polarized femtosecond laser pulses. We show that by optimizing the pulses’ parameters, a significant degree (∼10%) of enantioselective orientation can be achieved at 0 and 5 K rotational temperatures. This study suggests a set of reasonable experimental conditions for inducing and measuring strong enantioselective orientation. The strong enantioselective orientation and the wide availability of the femtosecond laser systems required for the proposed experiments may open new avenues for discriminating and separating molecular enantiomers.

We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters α. The system is prepared in a general quantum state by an evolution operator that depends on a set of unknown parameters P. After the preparation, the system evolves in time, and it is characterized by a time-dependent observable O(t). We show that it is possible to obtain closed-form expressions for the gradients of the distance between O(t) and a calculated observable with respect to α, P, and all elements of the system density matrix, whether for pure or mixed states. These gradients can be used in projected gradient descent to infer α, P, and the relevant density matrix from dynamical observables. We combine this approach with random phase wave function approximation to obtain closed-form expressions for gradients that can be used to infer population distributions from averaged time-dependent observables in problems with a large number of quantum states participating in dynamics. The approach is illustrated by determining the temperature of molecular gas (initially, in thermal equilibrium at room temperature) from laser-induced time-dependent molecular alignment.

We present a comprehensive study of enantioselective orientation of chiral molecules excited by a pair of delayed cross-polarized femtosecond laser pulses. We show that by optimizing the pulses' parameters, a significant (~ 10%) degree of enantioselective orientation can be achieved at zero and at five kelvin rotational temperatures. This study suggests a set of reasonable experimental conditions for inducing and measuring strong enantioselective orientation. The strong enantioselective orientation and the wide availability of the femtosecond laser systems required for the proposed experiments may open new avenues for discriminating and separating molecular enantiomers.

We present a theoretical-experimental study of polarization rotation of light traveling through a gas of fast-spinning molecules. The long-term behavior of the polarization angle can be used for probing relaxation dynamics in molecular gases.

We study the excitation of asymmetric-top (including chiral) molecules by two-color femtosecond laser pulses. In the cases of non-chiral asymmetric-top molecules excited by an orthogonally polarized two-color pulse, we demonstrate, classically and quantum mechanically, three-dimensional orientation. For chiral molecules, we show that the orientation induced by a cross-polarized two-color pulse is enantioselective along the laser propagation direction, namely, the two enantiomers are oriented in opposite directions. The classical and quantum simulations are in excellent agreement on the short time scale, whereas on the longer time scale, the enantioselective orientation exhibits quantum beats. These observations are qualitatively explained by analyzing the interaction potential between the two-color pulse and molecular (hyper-)polarizability. The prospects for using the enantioselective orientation for enantiomers' separation is discussed.

We theoretically study an impulsively excited quantum bouncer (QB)—a particle bouncing off a surface in the presence of gravity. A pair of time-delayed pulsed excitations is shown to induce a wave-packet echo effect—a partial rephasing of the QB wave function appearing at twice the delay between pulses. In addition, an appropriately chosen observable [here, the population of the ground gravitational quantum state (GQS)] recorded as a function of the delay is shown to contain the transition frequencies between the GQSs, their populations, and partial phase information about the wave-packet quantum amplitudes. The wave-packet echo effect is a promising candidate method for precision studies of GQSs of ultracold neutrons, atoms, and antiatoms confined in closed gravitational traps.

We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schrödinger equation. Our approach formulates the inverse problem as a target vector estimation problem and uses Bayesian surrogate models of the Schrödinger equation solutions to direct the optimization of feedback loops. For the surrogate models, we use Gaussian processes with vector outputs and composite kernels built by an iterative algorithm with the Bayesian information criterion (BIC) as a kernel selection metric. The outputs of the Gaussian processes are designed to model an observable simultaneously at different time instances. We show that the use of Gaussian processes with vector outputs and the BIC-directed kernel construction reduces the number of iterations in the feedback loops by, at least, a factor of 3. We also demonstrate an application of Bayesian optimization for inverse problems with noisy data. To demonstrate the algorithm, we consider the orientation and alignment of polyatomic molecules SO2 and propylene oxide (PPO) induced by strong laser pulses. We use simulated time evolutions of the orientation or alignment signals to determine the relevant components of the molecular polarizability tensors. We show that, for the five independent components of the polarizability tensor of PPO, this can be achieved with as few as 30 quantum dynamics calculations.

Short laser pulses are widely used for controlling molecular rotational degrees of freedom and inducing molecular alignment, orientation, unidirectional rotation, and other types of coherent rotational motion. To follow the ultrafast rotational dynamics in real time, several techniques for producing molecular movies have been proposed based on the Coulomb explosion of rotating molecules, or recovering molecular orientation from the angular distribution of high harmonics. The present work offers and demonstrates a novel nondestructive optical method for direct visualization and recording of movies of coherent rotational dynamics in a molecular gas. The technique is based on imaging the time-dependent polarization dynamics of a probe light propagating through a gas of coherently rotating molecules. The probe pulse continues through a radial polarizer, and is then recorded by a camera. The technique is illustrated by implementing it with two examples of time-resolved rotational dynamics: alignment–antialignment cycles in a molecular gas excited by a single linearly polarized laser pulse, and unidirectional molecular rotation induced by a pulse with twisted polarization. This method may open new avenues in studies on fast chemical transformation phenomena and ultrafast molecular dynamics caused by strong laser fields of various complexities.

Echoes occur in many physical systems, typically in inhomogeneously broadened ensembles of nonlinear objects. They are often used to eliminate the effects of dephasing caused by interactions with the environment as well as to enable the observation of proper, inherent object properties. Here, we report the experimental observation of quantum wave-packet echoes in a single, isolated molecule. The entire dephasing-rephasing cycle occurs without any inhomogeneous spread of molecular properties, or any interaction with the environment, and offers a way to probe the internal coherent dynamics of single molecules. In our experiments, we impulsively excite a vibrational wave packet in an anharmonic molecular potential and observe its oscillations and eventual dispersion with time. A second, delayed pulse gives rise to an echo-a partial recovery of the initial coherent oscillations. The vibrational dynamics of single molecules is visualized by a time-delayed probe pulse dissociating them, one at a time. Two mechanisms for the echo formation are discussed: a.c. Stark-induced molecular potential shaking and creation of a depletion-induced 'hole' in the nuclear spatial distribution. The single-molecule wave-packet echoes may lead to the development of new tools for probing ultrafast intramolecular processes in various molecules.Following an impulsive laser excitation of a single molecule, a dispersed vibrational wave-packet is partially rephased by a second pulse, and a wave-packet echo is observed. This wave-packet echo probes ultrafast intramolecular processes in the isolated molecule.

We report on the first experimental demonstration of enantioselective rotational control of chiral molecules with a laser field. In our experiments, two enantiomers of propylene oxide are brought to accelerated unidirectional rotation by means of an optical centrifuge. Using Coulomb explosion imaging, we show that the centrifuged molecules acquire preferential orientation perpendicular to the plane of rotation, and that the direction of this orientation depends on the relative handedness of the enantiomer and the rotating centrifuge field. The observed effect is in agreement with theoretical predictions and is reproduced in numerical simulations of the centrifuge excitation followed by Coulomb explosion of the centrifuged molecules. The demonstrated technique opens new avenues in optical enantioselective control of chiral molecules with a plethora of potential applications in differentiation, separation, and purification of chiral mixtures.

We explore a pure optical method for enantioselective orientation of chiral molecules by means of laser fields with twisted polarization. Several field implementations are considered, including a pair of delayed, cross-polarized laser pulses, an optical centrifuge, and polarization-shaped pulses. We show that these schemes lead to out-of-phase time-dependent dipole signals for different enantiomers, and we also predict a substantial permanent molecular orientation persisting long after the laser fields are over. The underlying classical orientation mechanism common to all of these fields is discussed, and its operation is demonstrated for a range of chiral molecules of various complexity: hydrogen thioperoxide (HSOH), propylene oxide (CH3CHCH2O), and ethyl oxirane (CH3CH2CHCH2O). The presented results demonstrate generality, versatility, and robustness of this optical method for manipulating molecular enantiomers in the gas phase.

In recent years, several femtosecond laser techniques have been developed that can make gas molecules rotate extremely fast, whereas the gas stays translationally cold. Herein we use molecular-dynamics simulations to investigate the collisional dynamics of gases of such molecules (superrotors). We found that the common route of superrotors to equilibrium is rather generic. It starts with a long-lasting gyroscopic stage, during which the molecules keep their fast rotation and the orientation of their angular momentum despite the many collisions they undergo. The inhibited rotational relaxation is characterized by a persistent anisotropy in the molecular angular distribution, manifested in long-lasting optical birefringence and in anisotropic diffusion of the gas. Later, the gyroscopic stage is abruptly terminated by a self-accelerating explosive rotational-translational energy exchange that generates sound and macroscopic vortices with a hot rotating core.

We study the dynamics of paramagnetic molecular superrotors in an external magnetic field. An optical centrifuge is used to create dense ensembles of oxygen molecules in ultrahigh rotational states. In is shown, for the first time, that the gas of rotating molecules becomes optically birefringent in the presence of a magnetic field. The discovered effect of "magneto-rotational birefringence" indicates the preferential alignment of molecular axes along the field direction. We provide an intuitive qualitative model, in which the influence of the applied magnetic field on the molecular orientation is mediated by the spin-rotation coupling. This model is supported by the direct imaging of the distribution of molecular axes, the demonstration of the magnetic reversal of the rotational Raman signal, and by numerical calculations.

We present a quantum localization phenomenon that exists in periodically kicked three-dimensional rotors, but is absent in the commonly studied two-dimensional ones: edge localization. We show that under the condition of a fractional quantum resonance there are states of the kicked rotor that are strongly localized near the edge of the angular momentum space at J=0. These states are analogs of surface states in crystalline solids, and they significantly affect resonant excitation of molecular rotation by laser pulse trains.

We present full quantum mechanical scattering calculations using spinning molecules as target states for nuclear spin selective atom-diatom scattering of reactive D+H₂ and F+H₂ collisions. Molecules can be forced to rotate uni-directionally by chiral trains of short, non-resonant laser pulses, with different nuclear spin isomers rotating in opposite directions. The calculations we present are based on rotational wavepackets that can be created in this manner. As our simulations show, target molecules with opposite sense of rotation are predominantly scattered in opposite directions, opening routes for spatially and quantum state selective scattering of close chemical species. Moreover, two-dimensional state resolved differential cross sections reveal detailed information about the scattering mechanisms, which can be explained to a large degree by a classical vector model for scattering with spinning molecules.

The paper explores the prospects of observing the phenomenon of dynamical Anderson localization via nonresonant Raman-type rotational excitation of molecules by periodic trains of short laser pulses. We define conditions for such an experiment and show that current femtosecond technology used for nonadiabatic laser alignment of linear molecules is sufficient for this task. Several observables which can serve as indicators for Anderson localization are suggested for measurement, and the influence of experimental limitations imposed by the laser intensity noise, finite pulse duration, limited number of pulses in a train, and thermal effects is analyzed.

We show that molecules kicked periodically by laser pulses currently used in molecular alignment experiments allow to observe effects of the periodically kicked quantum rotor in a real rotational system. Among these effects are Anderson localisation in angular momentum and the scaling of the quantum resonance. Based on this, we propose a new scheme for selective molecular rotational excitation.

We show that the current laser technology used for field-free molecular alignment via impulsive Raman rotational excitation allows for observing long-discussed nonlinear quantum phenomena in the dynamics of the periodically kicked rotor. This includes the scaling of the absorbed energy near the conditions of quantum resonance and Anderson-like localization in the angular momentum. Based on this, we show that periodic trains of short laser pulses provide an efficient tool for selective rotational excitation and alignment in a molecular mixture. We demonstrate the efficiency of this approach by applying it to a mixture of two nitrogen isotopologues (14N ₂ and 15N ₂), and show that strong selectivity is possible even at room temperature.

We experimentally investigate the effect of quantum resonance in the rotational excitation of the simplest quantum rotor-a diatomic molecule. Using the techniques of high-resolution femtosecond pulse shaping and rotational state-resolved detection, we measure directly the amount of energy absorbed by molecules interacting with a periodic train of laser pulses, and study their dependence on the train period. We show that the energy transfer is significantly enhanced at quantum resonance, and use this effect to demonstrate selective rotational excitation of two nitrogen isotopologs, N214 and N215. Moreover, by tuning the period of the pulse train in the vicinity of a fractional quantum resonance, we achieve selective rotational excitation of para- and ortho-isomers of N215.

The effects of laser-induced pre-alignment on the deflection of paramagnetic molecules by inhomogeneous static magnetic field are studied. Depending on the relevant Hunds coupling case of the molecule, two different effects were identified: either suppression of the deflection by laser pulses (Hunds coupling case (a) molecules, such as ClO), or a dramatic reconstruction of the broad distribution of the scattering angles into several narrow peaks (for Hunds coupling case (b) molecules, such as O₂ or NH). These findings are important for various applications using molecular guiding, focusing and trapping with the help of magnetic fields.

In recent years it has become possible to align molecules in free space using ultrashort laser pulses. Here we explore two schemes for controlling molecule-surface scattering processes and which are based on laser-induced molecular alignment. In the first scheme, a single ultrashort nonresonant laser pulse is applied to a molecular beam hitting the surface. This pulse modifies the angular distribution of the incident molecules and causes the scattered molecules to rotate with a preferred sense of rotation (clockwise or counterclockwise). In the second scheme, two properly delayed laser pulses are applied to a molecular beam composed of two chemically close molecular species (isotopes, or nuclear-spin isomers). As the result of the double-pulse excitation, these species are selectively scattered to different angles after the collision with the surface. These effects may provide new means for the analysis and separation of molecular mixtures.

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series (Wölk et al 2011 New J. Phys. 13 103007): (i) A two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) A chirped one-photon transition in a two-level atom with a periodically modulated excited state and (iii) A linearly chirped onephoton transition driven by a sequence of ultrashort pulses. For each of these quantum systems, we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules on how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state.

We provide a theory of the deflection of polar and nonpolar rotating molecules by inhomogeneous static electric field. Rainbowlike features in the angular distribution of the scattered molecules are analyzed in detail. Furthermore, we demonstrate that one may efficiently control the deflection process with the help of short and strong femtosecond laser pulses. In particular, the deflection process may be turned off by a proper excitation, and the angular dispersion of the deflected molecules can be substantially reduced. We study the problem both classically and quantum mechanically, taking into account the effects of strong deflecting field on the molecular rotations. In both treatments we arrive at the same conclusions. The suggested control scheme paves the way for many applications involving molecular focusing, guiding, and trapping by inhomogeneous fields. (C) 2011 American Institute of Physics. [doi:10.1063/1.3535600]

We study the optimal focusing of two-level atoms with a near-resonant standing wave light, using both classical and quantum treatments of the problem in the thin-and thick-lens regimes. It is found that the near-resonant standing wave focuses the atoms with a reduced background in comparison with far-detuned light fields. For some parameters, the quantum atomic distribution shows even better localization than the classical one. Spontaneous emission effects are included via the technique of quantum Monte Carlo wave function simulations. We investigate the extent to which nonadiabatic and spontaneous emission effects limit the achievable minimal size of the deposited structures.

We present a new approach to nonresonant laser deceleration and cooling of atoms based on their interaction with a bistable optical cavity. The cooling mechanism presents a photonic version of Sisyphus cooling, in which the conservative motion of atoms is interrupted by sudden transitions between two stable states of the cavity mode. The mechanical energy is extracted due to the hysteretic nature of those transitions. The bistable character of the cavity may be achieved by an external feedback loop, or by means of nonlinear intracavity optical elements. In contrast to the conventional cavity cooling, in which atoms experience a viscoustype force, bistable cavity cooling imitates "dry friction" and stops atoms much faster. Based on this novel approach, we explore the prospects of using optical bistability for efficient radiation pressure cooling of micromechanical devices that are modeled as a Fabry-Perot resonator with one fixed and one oscillating mirror. In all cases, analytical results are presented, supported by realistic numerical examples.

We propose a generic approach to nonresonant laser cooling of atoms and molecules in a bistable optical cavity. The method exemplifies a photonic version of Sisyphus cooling, in which the matter-dressed cavity extracts energy from the particles and discharges it to the external field as a result of sudden transitions between two stable states.

We factor the number 157573 using an NMR implementation of Gauss sums. Although the current implementation is classical and scales exponentially, we believe that an extension to the quantum regime using entangled states is possible.

We present two physical systems which make Gauß sums experimentally accessible. The probability amplitude for a two-photon transition in an appropriate ladder system driven by a chirped laser pulse is determined by a Gauß sum. The autocorrelation function of a quantum rotor is also of the form of a Gauß sum. These examples suggest rules for determining prime factor components on the basis of the properties of Gauß sums. Moreover, we show how Gauß sums are related to the Riemann Zeta function.

We show that field-free molecular orientation induced by a half-cycle pulse may be considerably enhanced by an additional laser pulse inducing molecular antialignment. Two qualitatively different enhancement mechanisms are identified, depending on the pulse order, and their effects are optimized with the help of quasiclassical as well as fully quantum models.

We propose a novel generic approach to laser cooling based on the nonresonant interactions of atoms and molecules with optical standing waves experiencing sudden phase jumps. The technique, termed "optical shaking," combines the elements of stochastic cooling and Sisyphus cooling. An optical signal that measures the instantaneous force applied by the standing wave on the ensemble of particles is used as feedback to determine the phase jumps. This guarantees a drift towards lower energies and higher phase-space density without the loss of particles typical of evaporative cooling.

Coherence observation by interference noise (COIN) was used to measure fractional wave packet motion of thermal iodine. COIN interferograms were presented for different excitation wavelengths to analyze fractional vibrational revivals. The simulation results showed that the complex temporal structure of the observed fluorescence included rapid initial damping in short-time regime. The observation of the wave packets on long time scale indicated a delicate balance between rotational and vibrational molecular coherences.

We study the temporal behavior of generic transient signals originating from multilevel quantum systems. Such signals typically arise in the physics of wave packets in atoms, molecules, cavity QED, and ion traps and consist of a sum of a large number of harmonics whose frequencies depend nonlinearly on the sequential number of the harmonic. In particular, we focus on the semiclassical limit. Here, quantum beats between individual terms in the underlying sum lead to characteristic features of the signal in different time regimes, such as collapse, fractional revivals, and full revivals. We present a universal recipe for describing analytically all of the details of these features. Our approach is based on a specific representation of the sum of harmonics, which is most convenient in each of these time regions of interest. This brings out in a most natural way the phenomenon of fractional revivals and full revivals and explains their fine structures observed in recent experiments.

A general analysis of an oscillator with periodic frequency modulation is given. It is shown that squeezing and excitation energy exponentially grow with the number of modulation cycles under the condition of parametric instability. This condition yields a prescription for maximized squeezing when the frequency is periodically swept in an adiabatic fashion, with an abrupt return to the initial frequency at the end of each period. The type of modulation considered is shown to have remarkably broad instability domains near arbitrarily high ratios of the oscillator period to the modulation cycle duration. This property stands in striking contrast to the rapid narrowing of the squeezing domains with the ratio of the pump frequency to that of the signal in existing parametric processes. We discuss a possible realization of the proposed scheme, based on frequency modulation of a cavity mode in the microwave domain by a periodic train of optical pulses, and show that extremely strong squeezing is feasible under rather moderate requirements.